A Note on Klein–gordon Equation in a Generalized Kaluza–klein Monopole Background

Radu, Eugen; Visinescu, Mihai

doi:10.1142/s0217732307024127

Cited by 3 publications

(4 citation statements)

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“…The topology of the horizon of SqKK black holes is S 3 , while it looks like four dimensional black holes with a circle as an internal space in the asymptotic region. SqKK black holes were originally derived as five-dimensional vacuum solutions in the context of Kaluza-Klein theory [11,12].Recently, much effort has been devoted to reveal the properties of squashed Kaluza-Klein black holes [13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29]. Since the horizons of these black holes have the same nature as the fivedimensional black holes, Hawking radiation and quasi-normal modes from SqKK black holes would be different from those seen in four-dimensional black holes even at low energy [22,27,28].…”

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Stability of squashed Kaluza-Klein black holes

et al. 2008

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The stability of squashed Kaluza-Klein black holes is studied. The squashed Kaluza-Klein black hole looks like a five dimensional black hole in the vicinity of horizon and and looks like a four dimensional Minkowski spacetime with a circle at infinity. In this sense, squashed Kaluza-Klein black holes can be regarded as black holes in the Kaluza-Klein spacetimes. Using the symmetry of squashed Kaluza-Klein black holes, SU (2) × U (1) ≃ U (2), we obtain master equations for a part of the metric perturbations relevant to the stability. The analysis based on the master equations gives a strong evidence for the stability of squashed Kaluza-Klein black holes. Hence, the squashed Kaluza-Klein black holes deserve to be taken seriously as realistic black holes in the Kaluza-Klein spacetime. PACS numbers: 04.50.+h, 04.70.BwRecently, higher dimensional black holes have attracted much attention. In particular, many exotic black holes in the asymptotically flat spacetime are found [1][2][3][4][5][6][7]. From a realistic point of view, however, the extra dimensions need to be compactified to reconcile the higher dimensional gravity theory with our apparently four-dimensional world. The higher dimensional spacetimes with compact extra dimensions are called Kaluza-Klein spacetimes. The black holes should reside not in the asymptotically flat spacetimes but the asymptotically Kaluza-Klein spacetimes. We call these 'Kaluza-Klein black holes'. It would be important to study Kaluza-Klein black holes in the general dimensions. In this paper, we will consider five dimensional Kaluza-Klein black holes as a first step.It is well known that the simplest five-dimensional Kaluza-Klein black hole is the black string which is the direct product of four dimensional Schwarzschild black hole and a circle [8]. The topology of the horizon of black strings is S 2 × S 1 . The stability analysis of black strings has been done, and it was shown that black strings are stable when the horizon radius is larger than the scale of compact extra dimension [9]. Because of the stability, black strings are natural candidate of Kaluza-Klein black holes.Interestingly, another possibility has been recognized [10]. It is squashed Kaluza-Klein (SqKK) black holes that could also reside in the Kaluza-Klein spacetime. The topology of the horizon of SqKK black holes is S 3 , while it looks like four dimensional black holes with a circle as an internal space in the asymptotic region. SqKK black holes were originally derived as five-dimensional vacuum solutions in the context of Kaluza-Klein theory [11,12].Recently, much effort has been devoted to reveal the properties of squashed Kaluza-Klein black holes [13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29]. Since the horizons of these black holes have the same nature as the fivedimensional black holes, Hawking radiation and quasi-normal modes from SqKK black holes would be different from those seen in four-dimensional black holes even at low energy [22,27,28]. That means that the extra dimension can be o...

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Stability of squashed Kaluza-Klein black holes

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“…The MP spacetimes are members of more general classes, including: (i) the Israel-Wilson class [62]; (ii) higher-dimensional MP spacetimes [35]; (iii) the Kastor-Traschen class [63]. In each of these cases, the black holes are extremally charged.…”

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confidence: 99%

“…Contopoulos revealed that the binary MP spacetime exhibits selfsimilarity and chaotic dynamics [16][17][18][19][20][21][22]. Influential perspectives on the role of chaos in binary systems in relativity have followed from Yurtsever [23], Dettmann [24,25], Cornish [26,27], Frankel [28], Levin [29,30] and many others [31][32][33][34][35].…”

Section: Introductionmentioning

confidence: 99%

Binary black hole shadows, chaotic scattering and the Cantor set

Shipley¹,

Dolan²

2016

Class. Quantum Grav.

124

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We investigate the qualitative features of binary black hole shadows using the model of two extremally charged black holes in static equilibrium (a Majumdar-Papapetrou solution). Our perspective is that binary spacetimes are natural exemplars of chaotic scattering, because they admit more than one fundamental null orbit, and thus an uncountably infinite set of perpetual null orbits which generate scattering singularities in initial data. Inspired by the three-disc model, we develop an appropriate symbolic dynamics to describe planar null geodesics on the double black hole spacetime. We show that a one-dimensional (1D) black hole shadow may constructed through an iterative procedure akin to the construction of the Cantor set; thus the 1D shadow is self-similar.Next, we study non-planar rays, to understand how angular momentum affects the existence and properties of the fundamental null orbits. Taking slices through 2D shadows, we observe three types of 1D shadow: regular, Cantor-like, and highly chaotic. The switch from Cantor-like to regular occurs where outer fundamental orbits are forbidden by angular momentum. The highly chaotic part is associated with an unexpected feature: stable and bounded null orbits, which exist around two black holes of equal mass M separated by a 1 < a < √ 2a 1 , where a 1 = 4M/ √ 27. To show how this possibility arises, we define a certain potential function and classify its stationary points. We conjecture that the highly chaotic parts of the 2D shadow possess the Wada property.Finally, we consider the possibility of following null geodesics through event horizons, and chaos in the maximally extended spacetime. * joshipley1@sheffield.ac.uk

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“…Several aspects of SqKK black holes are also discussed, e.g. thermodynamics [48][49][50], Hawking radiation [51][52][53], gravitational collapse [54], behavior of the Klein-Gordon equation [55], stability for the neutral case [56] 1 , quasinormal modes [57,58], geodetic precession [59], Kerr/CFT correspondence [60] and gravitational lensing effects [61].…”

Section: Introductionmentioning

confidence: 99%

Stability analysis of squashed Kaluza–Klein black holes with charge

Nishikawa¹,

Kimura²

2010

Class. Quantum Grav.

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We study gravitational and electromagnetic perturbation around the squashed Kaluza-Klein black holes with charge. Since the black hole spacetime focused on this paper have SU (2) × U (1) ≃ U (2) symmetry, we can separate the variables of the equations for perturbations by using Wigner function D J KM which is the irreducible representation of the symmetry. In this paper, we mainly treat J = 0 modes which preserve SU (2) symmetry. We derive the master equations for the J = 0 modes and discuss the stability of these modes. We show that the modes of J = 0 and K = 0, ±2 and the modes of K = ±(J + 2) are stable against small perturbations from the positivity of the effective potential. As for J = 0, K = ±1 modes, since there are domains where the effective potential is negative except for maximally charged case, it is hard to show the stability of these modes in general. To show stability for J = 0, K = ±1 modes in general is open issue. However, we can show the stability for J = 0, K = ±1 modes in maximally charged case where the effective potential are positive out side of the horizon.call the higher-dimensional black holes on the spacetime with compact extra dimensions Kaluza-Klein black holes. In general, it is difficult to construct exact solutions describing Kaluza-Klein black holes because of the less symmetry than the asymptotically flat case.However, if we consider the spacetime with twisted extra-dimensions, we can construct such exact solutions, i.e. squashed Kaluza-Klein (SqKK) black holes [27,28] in the class of cohomogeneity-one symmetry. The topology of the horizon of this SqKK black holes is S 3 , while it looks like four-dimensional black holes with a circle as an internal space in the asymptotic region.Recently, much effort has been devoted to reveal the properties of squashed Kaluza-Klein black holes. In [29][30][31][32][33][34][35][36][37][38][39][40][41][42][43][44][45][46][47] generalizations of SqKK black holes are studied. Several aspects of SqKK black holes are also discussed, e.g. thermodynamics [48-50], Hawking radiation [51-53], gravitational collapse [54], behavior of Klein-Gordon equation [55], stabil-

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A Note on Klein–gordon Equation in a Generalized Kaluza–klein Monopole Background

Cited by 3 publications

References 23 publications

Stability of squashed Kaluza-Klein black holes

Stability of squashed Kaluza-Klein black holes

Binary black hole shadows, chaotic scattering and the Cantor set

Stability analysis of squashed Kaluza–Klein black holes with charge

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